# Research data supporting "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image". B-spline representation of static structure factor.

## Description

The files contain knots and coefficients of third order (quadratic) B-spline representation approximating the structure factor S(q) appearing in the equation for power spectral density of particle or cavity monolayer. The structure factor depends on the radial distribution function (RDF) of objects forming the monolayer. In our computations, we used a B-spline representation of the RDF computed for a hard disk system of surface coverage 0.85. The representation, averaged over 26 replicas of RDF, was calculated as described at http://dx.doi.org/10.17632/3csw4wmjnr.1. With the RDF representation, we numerically computed the structure factor using the procedure DBFQAD of SLATEC library. This way we got 1E5 values of the structure factor at equidistant wavenumbers in the interval from 1E-3 to 1E2. Finally, we fit a B-spline representation to the discrete function S(q). For that, we used the B-spline fitting procedure splrep of the package SciPy.interpolate included in the Python-based open-source library SciPy. We used a forth order (cubic) B-spline with the default knot vector generated by the procedure splrep, i.e., with the knot separation distance equal about 1E-3. To calculate the structure factor with the B-spline you can use the procedures splev or BSpline of the module SciPy.interpolate of SciPy library v. 1.7.1. The knot vector in the attached files begins and ends with three improper knots, in accordance with the requirements of the procedures. For details, see the paper: P. Weroński & K. Pałka, "Roughness spectroscopy of particle monolayer: Implications for spectral analysis of the monolayer image", Measurement 196 (2022) 111263.

## Files

## Steps to reproduce

To use the files, download the version for linux or windows and unzip it. You will get two files with self-explanatory names. To calculate the structure factor with the B-spline, use the procedures splev or BSpline of the module SciPy.interpolate of SciPy library v. 1.7.1 or compatible.